How to extend an Operator
@batFINGER: Thank you! It works.

I've done it like this now:

import bpy

class Base:
    strprop = bpy.props.StringProperty(default = "Test")

class MyOperator(bpy.types.Operator, Base):
    bl_idname = "object.my_operator"
    bl_label = "My Operator"

    def execute(self, context):
        print(self.strprop)
        return {'FINISHED'}

bpy.utils.register_class(MyOperator)